\begin{tabular}{l}
\text{\LARGE{Chi-squared distribution}}\\
\\\hline\\
\text{Chi-squared distribution with }k\text{ degrees of freedom is the distribution of}\\ 
\text{a sum of }k\text {independent standard normal random variables.}
\\\\\hline\\
\text{\Large{Input parameters}}\\
    \begin{array}{ll}\\
    \\k & \text{degrees of freedom}\\
    \end{array}
\\\\\hline\\
\text{\Large{Output parameters}}\\
    \begin{array}{ll}\\
    \\\text{Expected value} & \mathbf{k}\\
    \\\text{Standard deviation} & \mathbf{\sqrt{2k}}\\
    \\\text{Variance} & \mathbf{2k}\\
    \end{array}
\\\\\hline\\
\text{\Large{Additional information}}\\
    \begin{array}{ll}\\
    \\\text{Probability density function} & 
      \mathbf{\frac{\left(\frac{1}{2}\right)^{\frac{k}{2}}}{\Gamma\left(\frac{k}{2}\right)}x^{\frac{k}{2}-1}e^{\frac{-x}{2}}}\\
    \\\text{Moment-generating function} & \mathbf{\left(1-2t\right)^{-\frac{k}{2}}}\mbox{ for }\mathbf{2t<1}\\
    \end{array}
\end{tabular}